Abstract. By an application of the K.A.M. theory, we derive an accurate
normal form valid in the vicinity of partially hyperbolic tori which arise close
to simple resonances in nearly integrable Hamiltonian systems. This allows
precise estimates on the times of transition around the stable and unstable
manifolds of these tori. Hence, these normal forms provide an efficient tool
to compute the speed of drift of orbits shadowing a chain of hyperbolic tori
associated to a simple resonant curve in the action space.